[Haskell-cafe] traversal with an arrow
tom-lists-haskell-cafe-2017 at jaguarpaw.co.uk
Sun Jun 19 08:15:09 UTC 2022
On Sun, Jun 19, 2022 at 01:28:14AM +0200, Olaf Klinke wrote:
> > On Fri, Jun 17, 2022 at 05:01:55PM +0200, Olaf Klinke wrote:
> > > Is there prior art to the following generalisation?
> > > traverseArrow :: Traversable t => a x y -> a (t x) (t y)
> > Perhaps you are looking for this:
> > https://github.com/tomjaguarpaw/Arrows2/issues/3#issuecomment-561973678
> Thanks Tom, can you explain what's behind this implementation, for
> those unfamiliar with arrow syntax? I guess [*] that the Traversal type
> used is a manifestation of the fact that one can transform any
> traversable structure (t a) into ([a],t ()) and sort the contents of
> the linked list back into their original places? This way, arbitrary
> traversals can be reduced to traversals over linked lists. Then the
> ArrowChoice is needed to pattern match on the list constructors?
Yes, that's about right, or perhaps more precisely:
"A 'Traversal a r b' is a structure that you can extract 'a's from, at
the same time replacing them with 'r's. The final result is a 'b'."
So, for example, if 'Traversable t' then 't a' is such a structure
(where b ~ t r). That's why there's a function
traversal :: Traversable t => t a -> Traversal a r (t r)
Hope that helps,
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